{"paper":{"title":"Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Oleksiy Khorunzhiy","submitted_at":"2015-12-30T19:09:19Z","abstract_excerpt":"We consider the ensemble of $N\\times N$ real random symmetric matrices $H_N^{(R)}$ obtained from the determinant form of the Ihara zeta function associated to random graphs $\\Gamma_N^{(R)}$ of the long-range percolation radius model with the edge probability determined by a function $\\phi(t)$.\n  We show that the normalized eigenvalue counting function of $H_N^{( R)}$ weakly converges in average as $N,R\\to\\infty$, $R=o(N)$ to a unique measure that depends on the limiting average vertex degree of $\\Gamma_N^{(R)}$ given by $\\phi_1 = \\int \\phi(t) dt$. This measure converges in the limit of infinit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09065","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}